matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2_plus.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "basic_2A/multiple/mr2.ma".
  16
  17 (* MULTIPLE RELOCATION WITH PAIRS *******************************************)
  18
  19 let rec pluss (cs:list2 nat nat) (i:nat) on cs ≝ match cs with
  20 [ nil2          ⇒ ◊
  21 | cons2 l m cs ⇒ {l + i, m} @ pluss cs i
  22 ].
  23
  24 interpretation "plus (multiple relocation with pairs)"
  25    'plus x y = (pluss x y).
  26
  27 (* Basic inversion lemmas ***************************************************)
  28
  29 lemma pluss_inv_nil2: ∀i,cs. cs + i = ◊ → cs = ◊.
  30 #i * // normalize
  31 #l #m #cs #H destruct
  32 qed.
  33
  34 lemma pluss_inv_cons2: ∀i,l,m,cs2,cs. cs + i = {l, m} @ cs2 →
  35                        ∃∃cs1. cs1 + i = cs2 & cs = {l - i, m} @ cs1.
  36 #i #l #m #cs2 * normalize
  37 [ #H destruct
  38 | #l1 #m1 #cs1 #H destruct /2 width=3 by ex2_intro/
  39 ]
  40 qed-.